Question 375018
How many 10 digit numbers can be formed if the first three digits are 407
<pre>
There are two methods.  I'll do both.

----------------------------------------

The largest 10 digit number that has the first three digits 407 is

4079999999

and that number is the the number of positive integers from 1 to 4079999999,
inclusively.

We wish to subtract from that the number of integers less than that number
which do not have 407 as its first three digits.

The largest 10-digit number that does not have its first three digits as 407 is

4069999999

and that is the number of positive integers from 1 to 4069999999, inclusively.

So we subtract the second number from the first number:

 4079999999
-4069999999
-----------
   10000000

------------------------------------

Or we could do it as an arithmetic sequence:

{{{a[1]=4070000000}}}, {{{a[n]=4079999999}}}, {{{d=1}}}

Then use the formula

{{{a[n]=a[1]+(n-1)d}}}

{{{4079999999=4070000000+(n-1)(1)}}}

{{{4079999999=4070000000+n-1}}}

{{{4079999999=4069999999+n}}}

{{{10000000=n}}}

Edwin</pre>